Changes in risk appreciation, and short memory of house buyers when the market is hot, a case study of Christchurch, New Zealand

ABSTRACT

In this paper, house prices in Christchurch are analysed over three distinct periods of time: post-2011 earthquake, pre-COVID-19 lockdown, and post-COVID-19 lockdown. The first method used is the well-established hedonic price model, additionally a second method incorporates random effects into the model to capture unobserved heterogeneity in buyers’ preferences for certain features of a house. Results show that buyers, in periods that are temporally distant from the 2011 Christchurch earthquake, underappreciate the risk of potential earthquake damage to a property. We find that there are observable shifts in buyer preference across the different time periods, specifically in terms of section size. We also examine heterogeneity and correlations in buyers’ preferences for floor area, land area, and age of a property.

KEYWORDS:

• Hedonic house price model
• natural disaster
• New Zealand

Introduction

Many property markets around the world post-COVID-19 lockdowns are dominated by significant price inflation due to low interest rates. However, there is preliminary evidence of more complex changes than just an increase in prices. For example, some buyers seem to appreciate larger sections after being in lockdown. In this paper, we analyse preferences and marginal willingness to pay (MWP) of house buyers for different features of a property using the hedonic house price model. We account for heterogeneity of buyer preferences by including random coefficients in the model and estimate the joint distribution of random coefficients nonparametrically, which is the first instance of an application of this kind. We compare the property market over three periods. Relatively stable periods from 2014 to 2016, the period pre-COVID-19, and a hot market post COVID-19. We find that preferences change and buyers seem to have a different attitude towards risk associated with the location of the house.

One of our main findings is that in the period immediately following the 2011 earthquake, buyers were willing to pay more for locations that were known to have a relatively low risk of sustaining damage due to soil liquefaction in the event of another major earthquake. In the other periods, 9 – 10 years after the major Christchurch earthquake, the effects of this additional risk to the property were not as significant. We found that, post-lockdown, buyers were willing to pay more for a larger section size, compared to the pre-lockdown period.

The hedonic house price model is a very popular tool and has been widely used in the literature. It builds on hedonic price models for differentiated products introduced by Lancaster (1966). These models explain product prices as a function of observable product characteristics. Rosen (1974) connects the model to consumer demand in an equilibrium market, which allows to infer the consumer’s marginal willingness to pay for each product characteristic from observations of prices. The main assumptions necessary for this deduction are a market equilibrium, i.e. no consumer can increase their utility by choosing a different product. In addition, consumers are fully informed, free to choose any other product and to purchase a continuous level of each characteristic. For detailed discussions of these assumptions in the context of property markets see Palmquist (2005).

In Bajari and Benkard (2005) a two-step procedure is proposed for the estimation of consumer preferences in the hedonic model. The first step is to estimate the price function which maps product characteristics to prices. The second step is to estimate consumer preferences as the first derivative of the price function. We suggest a different approach by adopting a feature from the BLP demand model Berry et al. (1995). We introduce a linear model for the price function with random coefficients that vary across consumers. This assumes that each consumer has their own price function that depends on their preferences which correspond to the random coefficients. We estimate the joint densities of random coefficients nonparametrically using the penalised maximum likelihood approach in Mendoza et al. (2021), Dunker et al. (2021). Results of this analysis are available in the Appendix.

In relation to how this assumption interacts with auction theory, i.e. how does common value fit in with the assumption that every buyer has their own price function, we say that the real estate market in New Zealand, as most often is the case, contains aspects of both private and common value paradigms. Re-sale market value considerations as well as rental suitability are definitely present. However, we assume a dominant private value environment where the common value aspects are embedded.

A large number of studies did use hedonic price theory to analyse the property market. We can just mention a few. Heteroskedasticity in the hedonic price model induced by dwelling age is explored in Goodman and Thibodeau (1995) which describes a vintage effect that drives up a house’s price. An extension is Fletcher et al. (2000) which identifies other possible sources of heteroskedasticity, specifically the area of the property. Another important work using the hedonic price model is spatial autocorrelation and spatial heterogeneity. In Dubin (1992), using data from Baltimore, a new approach to evaluating the strength of the effect of spatially related variables such as neighbourhood quality and accessibility is implemented. The method builds on the hypothesis that the spatial auto-correlation in the error term will reveal the effect of neighbourhood quality and accessibility when they are left out as initial explanatory variables. In Helbich et al. (2014), the importance of spatial heterogeneity is demonstrated in the case of Austria, where it was shown that effects of variables can be overestimated if spatial effects are not considered. The hedonic house price model has also been used to examine the effects of specific characteristics of a house on its price. The effect of transportation infrastructure on house prices in Sydney, Australia was examined in Lieske et al. (2021). The effect of upzoning on house prices in Auckland, New Zealand was examined Greenaway McGrevy et al. (2021). And the effects of school zones and proximity to cellular towers on house prices in New Zealand were examined in Rehm and Filippova (2008), and Filippova and Rehm (2011). In Limsombunchai (2004) the hedonic model was compared to an Artificial Neural Network (ANN) in terms of predictive capability based on Christchurch data.

Data

The data consists of log real house prices and a selection of structural, neighbourhood, and locational characteristics. The data were obtained from a variety of different sources. Data such as nominal sales prices, dates of sale, structural characteristics, and zoning were obtained through TradeMe and QV. Real house prices are obtained by dividing the nominal house prices by the House Price Index (HPI) obtained from the Reserve Bank of New Zealand. Geospatial related characteristics, such as distance to schools, and the CBD were obtained by geocoding the addresses through the Google maps API and calculating the Haversine distance between two pairs of longitudes and latitudes.

Another very important geospatial characteristic is the technical category (TC) of the land on which a property is built on. The technical category is a classification of land that indicates the likelihood of a property to experience soil-liquefaction related damage in the event of an earthquake. TC1 zones are the least likely to sustain liquefaction-related damage, and TC3 zones face the possibility of significant damage related to liquefaction in the future event of a significant earthquake, with TC2 zones in between. These data were obtained from Canterbury Maps Open Data.

The 2013 and 2018 New Zealand Deprivation Indices, which are comprised of a variety of measures of deprivation, such as income, education, and housing quality, Atkinson et al. (2019), were used as features that represent the overall condition of a neighbourhood. The index was used as a proxy variable for how good the area is to live in. The deprivation index is available at a meshblock level, which is the smallest geographical unit for which statistical information is collected, see Atkinson et al. (2019).

The 2010 New Zealand school zones were obtained from Koordinates, which is an open access database for geographic data, as a geographical comma delimited file. The geocoded properties were then assigned using their latitudes and longitudes to determine if they lie within the polygonal area of a specific school zone. In 2019, new demarcations for school zones were issued and initially made known. These changes have not taken effect as of 2021. The data is also not yet available in an open access format. However, the changes may have already affected property prices. We kept this in mind when comparing the effects of school zones across different time frames.

The data were cleaned and filtered before they were used for model fitting. Three subsets were constructed based on different time periods, 1 January 2014 to 31 December 2015, 1 March 2019 to 29 February 2020, and 1 May 2020 to 30 June 2021. The first time period corresponds to a time frame that is close to the 2011 earthquake that caused significant damage to a large number of properties in Christchurch but is a period where the property market returned to stable conditions. The second time period corresponds to a time frame that is temporally distant from the 2011 earthquake and before the 2020 nationwide lockdown due to COVID-19. The final time period corresponds to a time period after the easing of lockdown restrictions and when the market was turning hot.

To ensure that there were no erroneous entries and significant outliers, sensible filters were applied. Properties whose distance to the CBD was greater than 15 kilometres were removed to ensure only properties within Christchurch were considered. Properties with floor areas less than $60{\mathrm{m}}^2$, land areas less than $200{\mathrm{m}}^2$, and land areas greater than $3000{\mathrm{m}}^2$ were removed.

Furthermore, only ‘Residential Suburban’ properties were used. This was done in order to control for the unobserved effects attached to different zoning codes, as it carries with it different rules for land use. Properties used in the analysis were also limited to those that have assigned technical categories. The summary of features used as input data for the pre-lockdown period can be seen in Table 1, and the additional tables for other time periods can be found in the Appendix.

Table 1. Input data for pre-lockdown period $\mathit{n}=1091$.

Variable	Data Type	Min	Max	Mean	Std. Dev.
Log Real Price	Floating point	4.719	7.588	5.298	0.337
Bedrooms	Integer	2	9	–	0.794
Bathooms	Integer	1	4	–	0.608
Toilets	Integer	1	4	–	0.773
Carparks	Integer	1	6	–	0.567
Floor Area	Floating Point	62.0${\mathrm{m}}^2$	498.0${\mathrm{m}}^2$	161.6${\mathrm{m}}^2$	64.031
Land Area	Floating Point	219.0${\mathrm{m}}^2$	2925.0${\mathrm{m}}^2$	690.8${\mathrm{m}}^2$	203.880
Position of Property	Categorical	–	–	–	–
Roof Condition	Categorical	–	–	–	–
View from Property	Categorical	–	–	–	–
Wall Condition	Categorical	–	–	–	–
Dist. CBD	Floating point	0.237$\mathrm{km}$	13.498$\mathrm{km}$	6.018$\mathrm{km}$	1.927
Dist. to Secondary	Floating point	0.101$\mathrm{km}$	8.841$\mathrm{km}$	1.760$\mathrm{km}$	1.213
Dist. to Secondary	Floating point	0.101$\mathrm{km}$	8.841$\mathrm{km}$	1.760$\mathrm{km}$	1.213
Technical Category	Categorical	–	–	–	–
Age Purchased	Integer	0	119	47.67	25.884
NZ Deprivation Score	Integer	846	1249	969.9	70.870
School Zone	Categorical	–	–	–	–
Ward	Categorical	–	–	–
(Age Purchased)^2	Integer	0	14161	2941.890	2722.924

Finally, there is an important consideration to make when drawing conclusions derived from the subset of data spanning 2014–2016. Due to constraints and limitations in the process of obtaining the data, we were limited to using properties that were sold both in the period 2019–2021 and 2014–2016. This leads to some form of a selection bias, since there might be particular qualities that are associated with properties that are resold at a higher frequency. However, the effect of this is not within the scope of the study, and we assume the case that the selection bias has minimal impact on the specific analysis done in this paper.

Method

The first model considered is the standard multiple linear regression model given by the equation below,

(1) $\mathit{ln}\mathit{P}=\mathit{\beta }\mathbf{X}+\mathit{\epsilon }$(1)

where $\mathbf{X}$ is a matrix of regressors listed in 1, $\mathit{\beta }$ is a vector of slopes and an intercept, $\mathit{\epsilon }$ is the error term, and $\mathit{P}$ are the real property prices.

An important consideration in fitting the hedonic model is omitted-variable bias that manifests as spatial correlation, Bishop et al. (2020). One variable of interest, technical category (TC) is an inherently spatial characteristic of a residential property. Great care was taken in specifying the model to prevent misattributing variation in the response variable to TC rather than other spatial characterstics. However, it is unlikely that all attributes of a property that are geographically determined can be accounted for.

An approach suggested by Bishop et al. (2020) to address the problem of omitted-variable bias is to assign a dummy variable that determines the geographical location of a property such as as a zip code, or a suburb. We follow the methodology in Gibson et al. (2007) where the wards in which properties are included as a variable.

We have investigated the use of suburbs as the geographical feature mainly used to capture additional variation in the response due to geographical location; however, while the use of suburbs does better specify the model indicated by an increase in the model’s R-squared it also introduces the problem of collinearity with the TC variable, and hence masks its effect. More specifically, in the 2020–2021 period subset of data, all TC1 classified properties are found in only 13 out of the 65 suburbs, and out of all the properties located in these suburbs included in the data set 74% are TC1. The two other subsets of data for the 2014–2016, and 2019–2020 periods have similar statistics. Given that this masks the effect of the variable that we are interested in, we opted to retain the usage of Wards as the geographical variable to account for variation in the response due to geographical location as was done in Gibson et al. (2007). A summary of the models, and the relevant contingency table is made available in the Appendix

It was made apparent in McClay and Harrison (2003), Gibson et al. (2007), and Rehm and Filippova (2008) that school zones are a significant driver of house prices in New Zealand. In our analysis, Burnside, Riccarton, Christchurch Girls’, and Christchurch Boys’ school zones were considered as in Gibson et al. (2007), and additionally we also included the Cashmere Highschool zone. These school zones were used as variables to account for the premium commanded by being located in these desirable school zones.

Ideally, other environmental amenities would be included such as air quality and water quality as geographical features; however, these data are unavailable at the desired level of granularity.

Results and discussion

The results for the hedonic regression models are presented in Table A5. All the models for the periods 2014–2016, 2019–2020 (pre-lockdown), and 2020–2021 (post-lockdown) were significant at a 0.001 level. The models are all well-performing as each had an $\mathit{R}$-squared of 0.751, 0.808, and 0.823, respectively.

We focused our investigation on shifts in buyers’ marginal willingnesses to pay across the different time periods for certain structural attributes, changes in the assessment of risk of sustaining earthquake damage brought about by a property’s location, and the inclusion of random effects wherein we analysed the correlations between buyer preferences.

Locational and neighbourhood attributes such as school zones, deprivation, and wards primarily serve as control variables to prevent misattribution of variation to the locational variable of interest, technical category (TC). In-depth discussion on the effects of these control variables across the different models can be found in the appendix.

Analysis of the effect of school zoning on house prices in Christchurch has been done in McClay and Harrison (2003), and Gibson et al. (2007). The results that we obtained generally agree with the findings in those studies. As pointed out in Gibson et al. (2007), we likewise observed that there was an overemphasis on the effect of school zones when a significant amount of spatial autocorrelation is left unaccounted for. We note that this could be alleviated with the inclusion of a spatial dummy variable at a suburb level but would likely overspecify the model. Additional spatial dummy variables were not included as the effects of school zones are not the primary interest of this study, and we believe that the included variables serve as sufficient controls to discern the effect of technical category.

Structural attributes

Table 2 contains the regression estimates for each time period. Structural attributes such as the number of bedrooms, bathrooms, toilets, and carparks were generally insignificant for the periods 2014–2016 and pre-lockdown, while the number of bedrooms, and the number of toilets are significant at 0.001 and 0.01 levels, respectively, for the post-lockdown period. The insignificance of most of these structural attributes in the two periods is understandable as they are highly correlated with each other, and also with floor area and land area.

Table 2. Hedonic regression estimates by time period.

Variable	2014–2016	2019–2020	2020–2021
	Coefficient (SE)	Coefficient (SE)	Coefficient (SE)
Intercept	6.008*** (2.161e–1)	5.572*** (9.888e–;2)	5.622*** (8.017e–2)
Bedrooms	2.618e– (2.950e–2)	−3.748e–4 (1.129e-2)	−4.603e–2*** (9.502e–3)
Bathrooms	−2.615e–2 (3.580e–2)	2.963e–3 (1.551e–2)	2.236e–2† (1.247e–2)
Toilets	4.900e–2 (3.261e–2)	1.782e–2 (1.331e–2)	2.808e–2 ** (1.033e–2)
Carparks	2.227e–2 (1.895e–2)	2.790e–3 (9.303e–3)	1.616e–3 (6.807e–3)
Floor Area	1.876e–3***(3.674e–4)	2.202e–3*** (1.564e–4)	2.349e–3*** (1.238e–4)
Land Area	1.068e–4† (6.470e–5)	2.110e–4***(2.568e–5)	2.488e–4*** (2.113e–5)
RoofCondition Fair	1.559e–2 (2.292e–1)	2.704e–2 (7.450e–2)	−4.566e–2 (6.329e–2)
RoofCondition Good	3.587e–3 (4.956e–2)	−4.104e–3 (9.616e–3)	9.272e–3 (1.870e–2)
RoofCondition Mixed	−4.804e–1*** (9.930e–2)	−1.090e–1** (3.790e–2)	−1.843e–1*** (3.974e–2)
RoofCondition Poor	–	−1.812e–1 (1.543e–1)	2.334e–2 (1.474e–1)
View – Has view	1.037e–1 (6.841e–2)	2.768e–2 (2.552e–2)	4.307e–2† (2.235e–2)
WallCondition Fair	−2.271e–2 (1.881e–1)	−6.387e–2 (6.601e–2)	−2.066e–2 (5.095e–2)
WallCondition Good	2.197e–2 (4.873e–2)	7.225e–3 (2.360e–2	2.401e–2 (1.864e–2)
WallCondition Mixed	NA	NA	NA
WallCondition Poor	-	−5.496e–2 (1.537e–1)	NA
Dist. CBD	−4.302e–2*** (9.835e–3)	−1.597e–2*** (4.585e–3)	−2.910e–2*** (3.697e–3)
Dist. to Secondary	6.753e–2*** (1.248e–2)	2.738e–2*** (5.788e–3)	4.342e–2*** (4.847e–3)
TC2	−1.272e–1** (4.792e–2)	−2.129e–2 (2.102e–2)	−5.473e–2*** (1.659e–2)
TC3	−2.474e–1*** (5.107e-2)	−4.581e–2*(2.215e–2)	−4.065e–2* (1.789e–2)
Age Purchased	−2.146e–3 (2.102e–3)	−7.461e–3*** (8.331e–4)	−4.969e–3*** (6.875e–4)
(Age Purchased)^2	1.900e–5 (1.698e–5)	6.050e–5*** (7.117e–6)	4.010e–5*** (5.786e–6)
NZ Deprivation Score	−7.997e–4*** (1.818e–4)	−6.447e–4*** (8.399e–5)	−6.413e–4*** (6.813e–5)
Burnside	−1.354e–3 (9.992e–2)	1.085e–1** (4.094e–2)	2.100e–2 (3.449e–2)
BurnsideCHCBoys	1.589e–1 (1.418e–1)	3.011e–1*** (5.826e–2)	2.269e–1*** (4.709e–2)
BurnsideCHCBoysGirls	–	–	1.985e–1 (1.529e–1)
Cashmere	4.118e–2 (5.539e–2)	1.018e–1*** (2.204e–2)	6.988e–2*** (1.930e–2)
CHCBoys	1.356e–1 (1.413e–1)	2.277e–1*** (6.595e–2)	1.340e–1** (4.884e–2)
CHCGirlsBoys	3.945e–1** (1.289e–1)	4.478e–1*** (5.480e–2)	4.010e–1*** (4.461e–2)
Riccarton	−7.905e–2 (9.768e–2)	2.827e–2 (4.030e–2)	−6.785e–3 (3.288e–2)
RiccartonCHCBoys	–	3.320e–1* (1.574e–1)	–
RiccartonCHCGirlsBoys	–	–	3.681e–1* (1.527e–1)
Burwood	−3.579e–3 (3.608e–2)	−6.371e–2*** (1.647e–2)	−7.046e–2*** (1.366e–2)
Fendalton	2.001e–1 (1.218e–1)	1.161e–1* (5.051e–2)	1.777e–1*** (4.121e–2)
Linwood	−1.057e–1* (5.299e–2)	−1.012e–1*** (2.715e–2)	−1.255e–1 *** (2.142e–2)
Papanui	5.857e–2 (3.717e–2)	4.930e–2** (1.784e–2)	6.415e–2*** (1.498e–2)
Riccarton	1.441e–1 (1.011e–1)	5.760e–2 (4.362e–2)	1.009e–12** (3.645e–2)
Spreydon	2.075e–2 (4.384e–2)	1.575e–2 (2.369e–2)	8.456e–3 (1.917e–2)
Waimairi	7.987e–2 (9.164e–2)	4.538e–2 (3.733e–2)	8.145e–2** (3.193e–2)
Degrees of Freedom	316	1055	1474
$R^2$	0.751	0.808	0.823
$R^2$ adjusted	0.726	0.802	0.819
F–statistic	30.77	126.7	195.9

Table of coefficients for the model in different time periods. The legends ’***’ indicate significance at a 0.001 level, ’**’ indicates significance at a 0.01 level, ’*’ indicates significance at a 0.05 level, and ’†’ indicates significance at a 0.1 level.

At first glance, it seems peculiar that the number bedrooms has a negative effect on the price of a property with all else held equal, leading to approximately a 4.5% decrease in a property’s price for each additional bedroom unit. However, it is important to consider the context in which this interpretation is made, i.e. all other parameters are held constant. With this in mind, a plausible explanation is that the number of bedrooms could be less important than the size of these bedrooms from a buyer’s perspective. If floor area is held constant, an increase in the number of bedrooms limits the area of each bedroom and likewise other liveable parts of the house, which the data and model tell us is not desirable.

The floor area and land area of a property were significant for all the models up to a 0.001 level, with the sole exception of land area being significant only at a 0.1 level for the 2014–2016 period. The effects of these attributes across the three models are all positive as expected.

An interesting observation is that buyers’ willingness to pay for floor area and land area seems to be increasing over time. It is even more interesting to look at the difference in willingess to pay for land area between the pre-lockdown and post-lockdown periods which had a bigger change compared to the difference in the effect of floor area. It seems to suggest that buyers, post-lockdown, prefer a much larger section size than they did pre-lockdown. In the context of current events, this might be explained by the fact that a larger section size allows for more freedoms in the event of another strict lockdown.

Other structural attributes such as roof condition, wall condition mostly have an insignificant effect on the price of a property, except for a mixed roof condition. The reference levels used for roof condition and wall condition was ‘Average’. The resulting NA coefficient values for ‘WallCondition Mixed’ is due to it being collinear with ‘RoofCondition Mixed’, while the NA coeffecient for ‘WallCondition Poor’ is due to the fact that there was only one observation that had that specific classification.

While roof condition being ‘Mixed’ seems to have a strong negative effect on a property’s price, we hesitate to make any conclusions due to the limited number of observations classified in this category. There are 4, 15, and 18 observations under this classification for the 2014–2016, pre-lockdown, and post-lockdown periods, respectively. These properties also seem to not be spatially randomly distributed.

The effects of the estimated age of a property at purchase were negatively signed for all three time periods, while the squared estimated age was positively signed for all three models. This suggests that age has a depreciative effect on the price of a house up until a certain point, upon reaching a certain point the age of the property begins to have an appreciative effect, often called a vintage effect Goodman and Thibodeau (1995). We are able to observe this phenomenon in the three models, where age reduces the price until the vintage effect comes into play once a property reaches 56, 61, and 62 years old, respectively. Figure 1 illustrates this relationship clearly.

Figure 1. Net effect of age on the property price. Shows the effect of age in the depreciation of the property, and also shows the presence of the vintage effect.

Technical category

The effect of technical category (TC) underwent interesting changes across the three different time periods. As mentioned in Section 2, properties that had classifications of TC1, TC2, and TC3 were considered. The reference level for the model is TC1, which indicates the least risk of a property experiencing damage from soil liquefaction.

In the 2014 to 2016 period, TC2 and TC3 classifications were significant at 0.01 and 0.001 levels respectively. We are able to observe that the effects are negatively signed, and TC3 has a much stronger negative effect than TC2. The effects suggest that a classification of TC3 reduces a buyer’s willingness to pay by 11.9%, and TC3 reduces it by 21.9%. These results reflect the expected outcome as this time period is relatively close to 2011, and people were likely to exhibit caution when purchasing houses that could suffer damage in the event of another major earthquake.

For the pre-lockdown period, the effect of TC was significantly less compared to the previous time period. We found that by itself, it was no longer a significant predictor of a property’s price. In the case of the pre-lockdown model, only TC3 was significant at a 0.05 level. It retains its negative effect, and reduces a property’s price by approximately 4.5% which is much less compared to its effect during the 2014–2016 period.

In this time period, it would seem that buyers do not distinguish between properties that are classified as TC1 and TC2. The willingness to pay off buyers is also less affected if a property is classified as TC3. A possible explanation for this is that as time passes people perceive the risks involved as less important since the 2011 earthquake that highlighted these risks has become quite temporally distant.

For the post-lockdown period, the effect of TC was not what was expected. Both TC2 and TC3 were negatively signed and were significant at 0.001 and 0.05 levels, respectively. However, TC2 had a stronger negative effect on a buyer’s willingness to pay than if a property was classified as TC3. The effects suggest that a classification of TC2 reduces a buyer’s willingness to pay by 5.3%, and TC3 reduces it by 4%.

However, upon changing the reference level to TC2 instead of TC1, we observed that TC3 is not considered significantly different compared to TC2. This suggests that in the post-lockdown period buyers do not distinguish between properties classified as TC2 and TC3, which is a change from the pre-lockdown period where buyers did not distinguish between TC1 and TC2.

Conclusion

In this case study of the Christchurch housing market, we applied two models to analyse consumer preferences over three different time periods: the hedonic house price model and a two-step procedure that includes random coefficients for selected features in the hedonic model. The latter assumes that every buyer in the market has their own unique price function.

We observed significant shifts in consumer preferences across these three different time periods: 2014–2016, 2019–2020 pre-COVID-19 lockdown, and 2020–2021 post-COVID-19 lockdown.

In 2014–2016, a period relatively close to the 2011 earthquake, we found that a property’s locational attribute, the technical category (TC), which quantifies the risk of sustaining damage from soil liquefaction in the event of an earthquake, was a highly significant driver of house prices. The results showed that during this period a classification of TC3, which indicates the highest risk of damage among the TC classifications, reduces a buyer’s marginal willingness to pay by 21.9% on average, and a classification of TC2 reduces it by 11.9% on average. This changes in the following two periods which are much more temporally distant to the 2011 earthquake. In the pre-COVID-19 period, buyers did not distinguish between TC1 and TC2 properties, and the effect of a TC3 classification on a buyer’s marginal willingness to pay was significantly lower compared to the previous period. In the post-COVID-19 lockdown period, the effect of TC changed once again wherein buyers did not distinguish between TC2 and TC3 properties. These changes suggest that over the years, buyers have likely forgotten or have begun not to care about the risks associated with a property’s TC classification.

The hedonic model estimates for the effect of school zones are in agreement with the findings of McClay and Harrison (2003), and Gibson et al. (2007). It was pointed out by Gibson et al. (2007) that improper specification of spatial attributes can over-emphasise the effect of school zones, which we found to be true. However, including spatial dummy variables that are granular enough to differentiate between these spatial attributes may overspecify the model, especially given the significantly lower number of observations available to us for the 2014–2016 period. This is an area of the analysis that can be improved on.

The introduction of random coefficients into the model yielded some interesting insights into the structure of buyer preferences in the housing market. We observed a low to moderate negative correlation in buyer preferences for floor area and land area, which reflects the reality that, given a finite budget, these attributes serve as trade-offs for one another. The change in the expected value of the buyer preferences for floor area and land area over the two periods also agrees with the hedonic regression results, i.e. buyers seem to prefer larger living areas and larger section sizes in the post-lockdown market. We also observed a moderate to strong positive correlation in buyer preferences for floor area and dwelling age, which suggests that buyers are willing to pay more for an older house provided it has a larger floor area, and conversely buyers are willing to pay more for smaller houses provided that they are newer.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Appendix A

Table A1. Input data for post-lockdown period $\mathit{n}=1510$.

Variable	Data Type	Min	Max	Mean	Std. Dev.
Log Real Price	Floating point	4.709	7.610	5.294	0.343
Bedrooms	Integer	1	7	–	0.782
Bathooms	Integer	1	3	–	0.604
Toilets	Integer	1	6	–	0.802
Carparks	Integer	1	8	–	1.870
Floor Area	Floating Point	68.0${\mathrm{m}}^2$	563.0${\mathrm{m}}^2$	163.015${\mathrm{m}}^2$	66.0
Land Area	Floating Point	217.0${\mathrm{m}}^2$	2611.0${\mathrm{m}}^2$	693.9${\mathrm{m}}^2$	211.386
Roof Condition	Categorical	–	–	–	–
View from Property	Categorical	–	–	–	–
Wall Condition	Categorical	–	–	–	–
Dist. CBD	Floating point	1.579$\mathrm{km}$	14.301$\mathrm{km}$	7.3$\mathrm{km}$	1.990
Dist. to Secondary	Floating point	0.085$\mathrm{km}$	9.874$\mathrm{km}$	1.741$\mathrm{km}$	1.209
Technical Category	Categorical	–	–	–	–
Age Purchased	Integer	0	121	50.39	25.711
NZ Deprivation Score	Integer	839	1365	969.4	70.113
School Zone	Categorical	–	–	–	–
Ward	Categorical	–	–	–
(Age Purchased)^2	Integer	0	14641	3199.708	2790.211

Table A2. Input data for 2014–2015 $\mathit{n}=349$.

Variable	Data Type	Min	Max	Mean	Std. Dev.
Log Real Price	Floating point	4.728	6.794	5.497	0.346
Bedrooms	Integer	2	6	–	0.751
Bathooms	Integer	1	3	–	0.628
Toilets	Integer	1	4	–	0.793
Carparks	Integer	1	5	–	0.604
Floor Area	Floating Point	80.0${\mathrm{m}}^2$	430.0${\mathrm{m}}^2$	153.1${\mathrm{m}}^2$	62.199
Land Area	Floating Point	284.0${\mathrm{m}}^2$	2529.0${\mathrm{m}}^2$	686.5${\mathrm{m}}^2$	176.013
Position of Property	Categorical	–	–	–	–
Roof Condition	Categorical	–	–	–	–
View from Property	Categorical	–	–	–	–
Wall Condition	Categorical	–	–	–	–
Dist. CBD	Floating point	1.888$\mathrm{km}$	11.766$\mathrm{km}$	5.860$\mathrm{km}$	1.914
Dist. to Secondary	Floating point	0.097$\mathrm{km}$	8.762$\mathrm{km}$	1.665$\mathrm{km}$	1.272
Technical Category	Categorical	–	–	–	–
Age Purchased	Integer	2	120	52.47	24.103
NZ Deprivation Score (2013)	Integer	855	1286	958.1	70.170
School Zone	Categorical	–	–	–	–
Ward	Categorical	–	–	–
(Age Purchased)^2	Integer	0	14161	332.372	2641.848

Discussion locational attributes

Location-related features such as distance to the central business district (CBD), and the distance to a secondary school have consistent signs across the three different time periods and are significant to a 0.001 level. The negative effect of a property’s distance to the CBD is expected as property prices tend to increase based on how much more access to commercial amenities and work areas it has. We observe sizeable changes in the effect between time periods. A buyer’s willingness to pay for a property decreases by approximately 4.2%, 1.6%, and 2.9% for every additional kilometre farther away it is from the CBD for each time period respectively.

The positive effect of distance to a secondary school in the first place is unintuitive, as school accessibility in terms of distance is expected to have a positive influence on a property’s price. However, if we take into account the context of Christchurch, or even New Zealand as whole, being a place where privately driven vehicles are the most popular form of commuting the effect becomes understandable. Distance to a school matters less as students simply are driven by their parents to school. What we could be observing are the negative effects of being close to a secondary to school, such as increased traffic activity in the area at certain hours of the day due to students coming and going. This can also have measurable impacts on other aspects of quality of life, such as noise levels, overall air quality, etc.

The New Zealand deprivation index was significant at a 0.001 level for all three models and maintained a consistent negative effect throughout. It is important to note that the effect size for the deprivation index in the model for the 2014 to 2016 period is not directly comparable with that of the other two models since it uses the New Zealand deprivation index for 2013 instead of the one for 2018. There was no noticeable difference in the effect of the deprivation index between the two models for the pre-lockdown and post-lockdown periods. The effect size suggests that, all else equal, a property located in an area that has a deprivation score one unit higher would be 0.064% lower in price.

School zones in New Zealand are strong drivers of house price, as shown in McClay and Harrison (2003)Gibson et al. (2007), and Rehm and Filippova (2008). We observe similar findings here, further verifying the results in Gibson et al. (2007), wherein the premium that school zones command is greatly exaggerated if there is significant residual spatial autocorrelation left in the model.

The reference level for the school zone variable is ‘Other’, which indicates that a property does not belong in any of the five main school zones considered i.e. Burnside Highschool, Christchurch Boys’ Highschool, Christchurch Girls’ Highschool, Riccaroton Highschool, and Cashmere Highschool.

There is some difficulty in comparing the effects of school zones across different models, as it is entirely possible for a property to belong to multiple zones. This also leads to the possibility that, for a given time period, no property sold falls in a particular classification. This leads to the lack of coefficients for particular combinations of school zones. One thing to note is that the Christchurch Girls’ Highschool zone is completely enclosed in the Christchurch Boys’ Highschool zone, which effectively means that there are no properties that solely belong to the Christchurch Girls’ school zone. In this case, ‘CHCGirlsBoys’ effectively stands as the Christchurch Girls’ school zone.

For the period 2014 to 2016, ‘CHCGirlsBoys’ was signficantly different from the reference category at a 0.01 level. It was the only zone that was significantly different from the reference level for this period. The effect suggests that, all else held equal, a buyer is willing to pay up to a 48.3% premium for property that is in the Christchurch Girls’ Highschool zone as compared to an identically featured house that is not in any of the five considered school zones. This translates to approximately a $239,000 premium in price based on the median prices of properties that do not belong to any of the five school zones.

The lack of other significantly different school zones in the period 2014 to 2016 departs from the results seen in McClay and Harrison (2003), and Gibson et al. (2007), where Burnside Highschool, Christchurch Boys’ Highschool, and Riccarton Highschool zones all have significantly different effects on the price compared to the reference level. This change that we observe compared to the earlier studies may be due to some lingering effects of the 2011 Christchurch earthquake on buyers’ preferences, where home buyers prioritise different characteristics such as the Technical Category classification of the property.

For the pre-lockdown period, all but the Riccarton Highschool zone had significantly different effects on the price compared to the reference level. The school zone with the highest premium once again is that of Christchurch Girls’ Highschool, where consumers are willing to pay up to 56.5% more for a similarly featured property that is not within any of the five school zones. The other premiums that buyers are willing to pay are 11.5%, 10.7%, and 25.6% for properties in Burnside Highschool, Cashmere Highschool, and Christchurch Boys’ Highschool zones only, respectively.

During the post-lockdown period less school zones, or combinations thereof, were significantly different effects compared to the reference level. Once again, Christchurch Girls’ Highschool commands the highest premium where buyers are willing to pay 49.3% more compared to a non-zoned, identically featured house. The pre-lockdown estimates agree with the results of McClay and Harrison (2003), and Gibson et al. (2007) in terms of the significance of the effect of different school zones, while post-lockdown results do not. It could be the case that because the market has been much hotter in the months after the lockdown, school zones play a smaller role in the determination of a buyers’ decision to purchase a property.

The results for the effect sizes for which ward a property belongs in were generally expected. The reference level was ‘Other’, which indicates properties that do not belong in any of the seven considered wards. For the period 2014 to 2016, Linwood’s effect was negatively signed and significantly different from the reference category’s effect on price at a 0.05 level. It was the only ward that had a significantly different effect compared to the reference level. The effect suggests that a buyer’s willingness to pay for a property located in Linwood decreases by approximately 10% compared to a similarly featured property that is outside the seven wards.

The results for the pre-lockdown period suggest that the effect of which ward a property is located in assumed a greater role when it comes to determining a buyer’s willingness to pay compared to the 2014 to 2016 period.

During this period there were four wards that had significant effects on the price, namely Burwood, Linwood, Fendalton and Papanui. Linwood maintains a strong negative effect at a 0.001 level of significance which suggests that a property being in Linwood decreases a buyer’s willingness to pay by approximately 9.6%. A property being located in Fendalton had a strong positive effect which was significant to a 0.05 level. The effect suggests that buyers are willing to pay up to 12.3% more for a property that is located in Fendalton compared to one that is not within the seven wards. Being located in Burwood decreases the price of a property by approximately 6.1%, and being located in Papanui increases the price of a property approximately 5% compared to the reference category.

We observe a significant shift in the importance of ward classification in the post-lockdown period compared to the previous two periods. Every ward classification except for Spreydon had a significant effect on a buyer’s willingness to pay for a property. This shift in preferences aligns with the stipulation made above, where buyers, post-lockdown, experienced a change in priorities in terms of the qualities sought after in a property. We suspect that there are two main explanations for this shift in preferences. First, as mentioned in Section 2, new school zone demarcations were initially made known in 2019, which were set to take effect some time in 2022. What we might be observing is the effect of these boundary changes, as it entails significant changes in the scope of particular school zones compared to the data used for this paper, which would be the zoning schedule established in 2010. For example, Burnside Highschool’s zone effectively doubles when these changes take effect, which could possibly explain the insignificance of the effect of Burnside Highschool in the post-lockdown period.

Another plausible explanation is that given the market is hot the amount of transactions conducted by investors, not would-be homeowners, is likely to be higher than it would be if it were a buyer’s market.

In the post-lockdown period, the Fendalton ward once again commands the highest premium. Its effect is significant at a 0.001 level and suggests that buyers are willing to pay up to 19.4% more if a property is located in the Fendalton ward compared to a property that is not located in any of the other six wards. Linwood and Burwood retain their strong negative effects which are significant at a 0.001 level. Their effects suggest that prices of properties located in Linwood and Burwood decrease by approximately 11.8%, and 6.8%, respectively.

Unobserved heterogeneity

A second model used in analysing the data is a two-step procedure wherein we use a linear model for the price function with random coefficients. We allow the model to have two features that have random coefficients at a time and look at correlations in consumer preference between qualities of a property.

To implement this two-step procedure, a linear model is first fitted as in (3). We then let ${\mathbf{X}}_1$, and ${\mathbf{X}}_2$ be the vectors of regressors that have random effects to model the unobserved heterogeneity in consumer preferences. A new dependent variable, $\mathit{Y}$, is constructed using by adding back ${\mathbf{X}}_1$, and ${\mathbf{X}}_2$ or linear transformations thereof, to the residuals of the model as given below:

$\tilde{\mathit{Y}}=(\mathit{Y}-\hat{\mathit{Y}})+{\beta }_1{\mathbf{X}}_1+{\beta }_2{\mathbf{X}}_2.$

The regularised maximum likelihood method developed in Dunker et al. (2021), and Mendoza et al. (2021) is then used to nonparametrically estimate ${\hat{f}}_{\mathit{\beta }}$, the joint density distribution of the random coefficients, in the following model,

${\tilde{Y}}_{\mathit{i}}={\beta }_{0_i}+{\beta }_{1_i}{X}_{1_i}+{\beta }_{2_i}{X}_{2_i}.$

It was necessary to apply linear transformations on some features before estimation using regularised maximum likelihood in order to achieve stable solutions. For further elaboration on this we refer to Dunker et al. (2021).

Doing this assumes that every individual buyer has their own price function, which can provide interesting insights in terms of the variation in the buyer’s marginal willingness to pay for particular attributes associated with a property. This two-step procedure was only done for the pre-lockdown and post-lockdown periods, as there were not enough observations in the 2014 to 2016 period to yield stable solutions.

The pairs of features used for this analysis were: (1) floor area and land area, and (2) floor area and age at purchase. Features were standardised before they were used in the OLS model. As mentioned in Section 3, the application of linear transformations is often necessary to get proper coverage over the support of the joint-density, ${\hat{f}}_{\mathit{\beta }}$, being estimated. It is important to note that the estimates of OLS can be easily transformed back in the case where linear transformations are applied to the regressors.

The interpretation of the resulting estimate for ${\hat{f}}_{\mathit{\beta }}$ is that it is the joint distribution of buyers’ marginal willingness to pay off for an additional unit in the property features used in estimation. Summary statistics of the estimates for them are presented in Table A3 for the pre-lockdown period, and in Table A4 for the post-lockdown period.

The sign for the expected value of the random effect for age is not consistent with its OLS estimate for both the pre-lockdown and post-lockdown periods. Across the two time periods, the changes that the sizes of the effects underwent are consistent with that of the changes observed from the OLS estimates. Post-lockdown, people seem prefer or are willing to pay more for larger sections of land, and also more living space.

Table A3. Summary statistics of the estimates for $f_{\beta }$ for the pre-lockdown period.

Regressors	$\mathit{E}({\beta }_0)$	$\mathit{E}({\beta }_1)$	$\mathit{E}({\beta }_2)$	${\rho }_{{\beta }_1,{\beta }_2}$
Floor Area ($X_1$), Age at Purchase ($X_2$)	3.787e-1	1.289e-2	3.753e-4	0.407
Floor Area ($X_1$), Land Area ($X_2$)	3.406e-1	1.787e-3	3.637e-3	−0.318

Table A4. Summary statistics of the estimates for $f_{\beta }$ for the pre-lockdown period.

Regressors	$\mathit{E}({\beta }_0)$	$\mathit{E}({\beta }_1)$	$\mathit{E}({\beta }_2)$	${\rho }_{{\beta }_1,{\beta }_2}$
Floor Area ($X_1$), Age at Purchase ($X_2$)	3.271e-1	1.494e-2	6.897e-4	0.380
Floor Area ($X_1$), Land Area ($X_2$)	2.312e-1	1.460e-3	2.878e-3	−0.331

An interesting observation that can be made is that there is a negative correlation between the preferences of buyers with respect to floor area and land area. Figures A1 and A2 show the contour plots for the estimates for ${\hat{f}}_{\mathit{\beta }}$ for both time periods.

Figure A1. Contour plots of joint marginal distributions of ${\hat{f}}_{\mathit{\beta }}$ with floor area and land area having random effects: ${\hat{f}}_{{\beta }_0,{\beta }_1}$ (left), ${\hat{f}}_{{\beta }_0,{\beta }_2}$ (middle), ${\hat{f}}_{{\beta }_1,{\beta }_2}$ (right) pre-lockdown.

Figure A2. Contour plots of joint marginal distributions of ${\hat{f}}_{\mathit{\beta }}$ with floor area and land area having random effects: ${\hat{f}}_{{\beta }_0,{\beta }_1}$ (left), ${\hat{f}}_{{\beta }_0,{\beta }_2}$ (middle), ${\hat{f}}_{{\beta }_1,{\beta }_2}$ (right) post-lockdown.

The negative correlation suggests that there is a large group of buyers that have a preference for more floor area over more land area, and another large group of buyers with the opposite preference. In other words, this means that buyers generally prefer either more floor area or more land area, and not both at the same time.

Another interesting observation that can be drawn from Figures A1 and A2 is that according to the estimated distribution of the population there is a small portion of buyers that have negatively signed effects for both floor area and land area.

A possible explanation for this is that the model that was specified did not include spatial variables with a level of granularity that controls for all possible spatially related variation. For example, the suburb that a property belongs in is taken into account, it becomes sensible that a buyer might be willing to pay a much larger sum of money for a smaller house and a smaller section when it is located in a very affluent or popular suburb. While we did include the deprivation index as a proxy for how desirable it is to live in the area where the property is located, it does not capture the same information as the suburb in which the property is situated in. Another plausible explanation would be that this is simply a result of the regularisation that was applied.

Figure A3. Contour plots of joint marginal distributions of ${\hat{f}}_{\mathit{\beta }}$ with floor area and age at purchase having random effects: ${\hat{f}}_{{\beta }_0,{\beta }_1}$ (left), ${\hat{f}}_{{\beta }_0,{\beta }_2}$ (middle), ${\hat{f}}_{{\beta }_1,{\beta }_2}$ (right) pre-lockdown.

Figure A4. Contour plots of joint marginal distributions of ${\hat{f}}_{\mathit{\beta }}$ with floor area and age at purchase having random effects: ${\hat{f}}_{{\beta }_0,{\beta }_1}$ (left), ${\hat{f}}_{{\beta }_0,{\beta }_2}$ (middle), ${\hat{f}}_{{\beta }_1,{\beta }_2}$ (right) post-lockdown.

Figures A3 and A4 show the contour plots for the estimates for ${\hat{f}}_{\mathit{\beta }}$ for the case where floor area and age have random effects in both time periods. There is a moderate to strong correlation between the preferences of buyers for floor area and the age of a property.

This suggests that when a buyer is willing to pay more for an older house, they are also willing to pay more for more floor area. This means that buyers are mostly either willing to pay more for older houses provided that they have larger floor areas, or are willing to pay more for smaller houses provided that they are newer.

Additional OLS models

Table A5. Hedonic regression estimates by time period with quarterly time dummies.

Variable	2014–2016	2019–2020	2020–2021
	Coefficient (SE)	Coefficient (SE)	Coefficient (SE)
Intercept	1.381*** (2.241e-1)	1.347*** (1.664e-1)	1.361*** (8.197e-2)
Quarter 2	–	−3.952e–2 (2.755e–2)	−1.201e–1*** (1.148e–2)
Quarter 3	–	−1.434e–2 (1.546e–2)	−7.595e–2*** (1.099e–2)
Quarter 4	–	−9.093e–4 (1.094e–2)	−1.468e–3 (1.047e–2)
Quarter 1–2015	−5.323e–3 (4.677e–2)	–	–
Quarter 2–2014	−5.595e–2 (4.709e–2)	–	–
Quarter 2–2015	−3.348e–2 (4.420e–2)	–	-
Quarter 3–2014	−5.264e–3 (4.483e–2)	–	–
Quarter 3–2015	−2.400e–2 (4.525e–2)	–	–
Quarter 4–2014	−1.940e–2 (4.343e–2)	–	–
Quarter 4–2015	3.946e–2 (4.616e–2)	–	–
Bedrooms	1.319e–2 (3.197e–2)	−5.517e–3 (1.135e–2)	−5.443e–2*** (1.054e–2)
Bathrooms	−2.323e–2 (3.943e–2)	5.672e-3 (1.608e-2)	2.139e–2 † (1.290e–2)
Toilets	5.570e–3 (3.605e–2)	2.252e–2 (1.338e–2)	3.162e–2** (1.081e–2)
Carparks	3.271e–3 (2.089e–2)	3.585e–3 (9.361e–3)	4.090e–3 (7.016e–3)
Floor Area	2.943e–3***(3.950e–4)	2.203e–3*** (1.572e–4)	2.370e–3*** (1.276e–4)
Land Area	2.491e–4 (7.209e–5)	2.103e–4***(2.590e–5)	2.633e-4*** (2.180e-5)
RoofCondition Fair	2.079e–1 (2.475e–1)	2.958e–2 (7.482e–2)	−3.199e–2 (6.465e–2)
RoofCondition Good	−1.970e–2 (5.770e–2)	−2.847e–3 (2.364e–2)	1.134e–2 (1.896e–2)
RoofCondition Mixed	−5.561e–1*** (1.113e–1)	−1.127e–1** (3.809e–2)	−1.824e–1*** (4.058e–2)
RoofCondition Poor	–	−1.936e–1 (1.551e–1)	9.099e–3 (1.505e–1)
View – Has view	3.914e–2 (7.063e–2)	2.002e–2 (2.567e–2)	4.182e–2† (2.280e–2)
WallCondition Fair	−2.015e–1 (2.045e–1)	−8.691e–2 (6.663e–2)	−3.115e–2 (5.202e–2)
WallCondition Good	4.621e–2 (5.669e–2)	7.452e–3 (2.365e–2)	2.401e–2 (1.864e–2)
WallCondition Mixed	NA	NA	NA
WallCondition Poor	–	−8.832e–2 (1.547e–1)	NA
Dist. CBD	−4.389e–2*** (9.276e–3)	−1.632e–2*** (4.454e–3)	−2.713e–2*** (3.711e–3)
Dist. to Secondary	3.514e–2** (1.298e–2)	2.858e–2*** (5.767e–3)	4.112e–2*** (4.949e–3)
TC2	−4.404e–2 (3.399e–2)	−3.071e–2 (1.894e–2)	−4.129e–2** (1.567e–2)
TC3	−1.560e–1*** (3.943e–2)	−5.321e–2** (2.024e–2)	−2.798e–2 (1.711e–2)
Age Purchased	−6.723e–3** (2.206e–3)	−7.117e–3*** (8.395e–4)	−5.208e–3*** (7.137e–4)
(Age Purchased)^2	6.472e–5*** (1.899e–5)	5.841e–5*** (7.160e–6)	4.383e–5*** (5.999e–6)
NZ Deprivation Score	−8.780e–4*** (1.893e–4)	−6.433e–4*** (8.427e–5)	−6.206e–4*** (6.974e–5)
Burnside	−8.311e–2 (2.126e–1)	9.399e–2*** (2.577e–2)	3.261e–2 (2.217e–2)
BurnsideCHCBoys	4.097e–1† (2.116e–1)	2.914e–1*** (4.768e–2)	2.074e–1*** (3.975e–2)
BurnsideCHCBoysGirls	–	–	11.976e–1 (1.536e–1)
Cashmere	−1.624e–1 (1.247e–1)	9.841e–2*** (2.210e–2)	6.181e–2** (1.973e–2)
CHCBoys	−1.058e–2 (2.204e–1)	2.210e–1*** (5.415e–2)	1.356e–1** (4.247e–2)
CHCGirlsBoys	6.225e–1*** (1.305e–1)	4.331e–1*** (4.265e–2	3.938e–1*** (3.582e–2)
Riccarton	−1.016e–3 (3.112e–1)	2.827e–2 (4.030e–2)	–
RiccartonCHCBoys	–	3.320e–1* (1.574e–1)	–
RiccartonCHCGirlsBoys	–	–	–
Burwood	−5.058e–2 (3.608e–2)	−6.472e–2*** (1.654e–2)	−7.210e–2*** (1.393e–2)
Fendalton	–	1.214e–1** (3.975e–2)	1.878e–1*** (3.385e–2)
Linwood	−1.591e–1 (1.101e–1)	−1.034e–1*** (2.721e–2)	−1.350e–1*** (2.182e–2)
Papanui	−2.557e–2 (1.010e–1)	5.253e–2** (1.795e–2)	5.607e–2*** (1.533e–2)
Riccarton	2.063e–1 (3.678e–1)	7.751e–2* (3.064e–2)	1.066e–1*** (2.637e–2)
Spreydon	−5.600e–2 (9.363e–2)	1.570e–2 (2.378e–2)	1.510e–2 (1.964e–2)
Waimairi	1.125e–1 (2.313e–1)	5.472e–2 (2.774e–2)	8.780e–2*** (2.377e–2)
Degrees of Freedom	1054	1055	1462
$R^2$	0.7099	0.8056	0.8216
$R^2$ adjusted	0.6733	0.799	0.8172
F-statistic	19.39	121.3	187.1

Table of coefficients for the model in different time periods. The legends ’***’ indicate significance at a 0.001 level, ’**’ indicates significance at a 0.01 level, ’*’ indicates significance at a 0.05 level, and ’†’ indicates significance at a 0.1 level.

Additional results

Table A6 contains the summary results for the OLS models for each period when suburbs are used instead of wards as the geographic feature of each property. As mentioned in Section 3, the use of suburbs better specifies the model; however, the collinearity of the suburbs with the technical category of the property makes it unsuitable to be used in conjunction with TC which is the variable we are interested in looking at.

Table A6. Summary results for OLS models using suburb in place of wards as the geographical feature.

	2014–2016	2019–2020	2020–2021
Degrees of Freedom	267	1001	1407
R-squared	0.8378	0.8389	0.8594
Adj R-squared	0.7886	0.8246	0.8503
F-Statistic	17.03	58.56	94.51

Table A7 shows the contingency table for each period for the properties’ suburb and technical category. This table gives the view that if suburbs were to be used in place of wards as the geographical identifiers it will severely overlap with technical category in terms of the information that it retrieves, specifically in the case of TC1.

Table A7. Contigency table for suburb and technical category for each time period.

	2014–2016			2019–2020			2020–2021
Suburb	TC1	TC2	TC3	TC1	TC2	TC3	TC1	TC2	TC3
Aidanfield	0	2	0	0	9	0	0	18	0
Aranui	0	2	3	0	11	10	0	15	14
Avondale	0	3	2	0	1	13	0	4	22
Avonhead	13	0	0	49	0	0	66	0	0
Avonside	0	3	3	0	6	3	0	5	3
Beckenham	0	1	0	0	8	0	0	9	2
Belfast	0	3	0	0	8	0	0	7	1
Bishopdale	2	13	1	8	25	1	16	37	3
Bromley	0	2	0	0	9	0	0	13	0
Broomfield	6	0	0	8	0	0	14	0	0
Bryndwr	2	7	0	3	25	0	6	37	0
Burnside	13	1	0	34	10	1	58	7	1
Burwood	0	6	7	0	25	26	0	27	36
Casebrook	0	7	1	0	23	3	0	34	5
Cashmere	0	2	1	0	9	3	0	6	0
Cracroft				0	1	0	0	1	0
Dallington	0	2	5	0	5	4	0	10	10
Fendalton	0	6	1	0	10	10	0	30	6
Halswell	0	15	2	0	64	6	0	70	6
Harewood				2	13	0	0	14	0
Heathcote Valley	0	2	0	0	8	0	0	6	0
Hei Hei	6	0	0	17	0	0	16	0	0
Hillmorton	0	6	1	0	13	3	0	21	3
Hillsborough	0	2	0	0	5	1	0	8	1
Hoon Hay	0	20	0	0	33	0	0	50	2
Hornby	14	0	0	30	0	0	38	0	0
Huntsbury							0	1	0
Ilam	7	4	0	17	11	0	33	20	0
Islington	1	0	0	6	0	0	9	0	0
Kainga							0	1	0
Linwood	0	3	2	0	6	4	0	11	5
Mairehau	0	8	1	0	19	8	0	30	9
Merivale	0	0	4	0	3	11	0	2	14
Mount Pleasant				0	3	0	0	3	0
New Brighton	0	3	3	0	8	19	0	19	24
North New Brighton	0	4	2	0	7	8	0	14	11
Northcote	0	3	0	0	9	0	0	11	0
Northwood	0	2	2	0	12	4	0	15	9
Opawa	0	0	2	0	1	6	0	4	7
Papanui	0	7	0	0	17	0	0	38	0
Parklands	0	4	9	0	23	43	0	28	44
Redcliffs	0	1	0	0	2	1	0	3	2
Redwood	0	16	0	0	54	1	0	53	1
Riccarton				0	7	0	0	6	0
Richmond	0	0	3	0	2	8	0	2	13
Russley	5	0	0	14	0	0	15	0	0
Saint Martins	0	3	1	0	6	6	0	11	8
Shirley	0	11	2	0	18	2	0	31	3
Sockburn	2	0	0	18	0	0	18	0	0
Somerfield	0	2	0	0	19	0	0	9	0
South New Brighton	0	2	0	0	7	2	0	11	3
Southshore	0	0	1	0	4	6	0	3	2
Spreydon	0	2	0	0	6	0	0	3	0
St Albans	0	4	6	0	7	10	0	20	20
Strowan	0	6	0	0	9	1	0	23	3
Sumner	0	4	0	0	4	0	0	10	0
Sydenham				0	3	0	0	3	0
Templeton				4	0	0	12	0	0
Upper Riccarton	3	1	0	8	6	0	6	8	0
Waimairi Beach	0	2	0	0	8	0	0	7	0
Wainoni	0	0	5	0	2	8	0	6	9
Westmorland							0	1	0
Wigram	1	0	0	8	0	0	15	0	0
Woolston	0	3	4	0	16	8	0	25	12
Yaldhurst				2	0	0	2	0	0
Moncks Bay				0	3	0